720 research outputs found
Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure
The discrete-time mean-variance portfolio selection formulation, a
representative of general dynamic mean-risk portfolio selection problems, does
not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated
pre-committed efficient policy may become inefficient when considering the
corresponding truncated problem, thus stimulating investors' irrational
investment behavior. We investigate analytically effects of portfolio
constraints on time consistency of efficiency for convex cone constrained
markets. More specifically, we derive the semi-analytical expressions for the
pre-committed efficient mean-variance policy and the minimum-variance signed
supermartingale measure (VSSM) and reveal their close relationship. Our
analysis shows that the pre-committed discrete-time efficient mean-variance
policy satisfies TCIE if and only if the conditional expectation of VSSM's
density (with respect to the original probability measure) is nonnegative, or
once the conditional expectation becomes negative, it remains at the same
negative value until the terminal time. Our findings indicate that the property
of time consistency in efficiency only depends on the basic market setting,
including portfolio constraints, and this fact motivates us to establish a
general solution framework in constructing TCIE dynamic portfolio selection
problem formulations by introducing suitable portfolio constraints
Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection
The classical dynamic programming-based optimal stochastic control methods
fail to cope with nonseparable dynamic optimization problems as the principle
of optimality no longer applies in such situations. Among these notorious
nonseparable problems, the dynamic mean-variance portfolio selection
formulation had posted a great challenge to our research community until
recently. A few solution methods, including the embedding scheme, have been
developed in the last decade to solve the dynamic mean-variance portfolio
selection formulation successfully. We propose in this paper a novel mean-field
framework that offers a more efficient modeling tool and a more accurate
solution scheme in tackling directly the issue of nonseparability and deriving
the optimal policies analytically for the multi-period mean-variance-type
portfolio selection problems
Multi-Period Trading via Convex Optimization
We consider a basic model of multi-period trading, which can be used to
evaluate the performance of a trading strategy. We describe a framework for
single-period optimization, where the trades in each period are found by
solving a convex optimization problem that trades off expected return, risk,
transaction cost and holding cost such as the borrowing cost for shorting
assets. We then describe a multi-period version of the trading method, where
optimization is used to plan a sequence of trades, with only the first one
executed, using estimates of future quantities that are unknown when the trades
are chosen. The single-period method traces back to Markowitz; the multi-period
methods trace back to model predictive control. Our contribution is to describe
the single-period and multi-period methods in one simple framework, giving a
clear description of the development and the approximations made. In this paper
we do not address a critical component in a trading algorithm, the predictions
or forecasts of future quantities. The methods we describe in this paper can be
thought of as good ways to exploit predictions, no matter how they are made. We
have also developed a companion open-source software library that implements
many of the ideas and methods described in the paper
Bayesian emulation for optimization in multi-step portfolio decisions
We discuss the Bayesian emulation approach to computational solution of
multi-step portfolio studies in financial time series. "Bayesian emulation for
decisions" involves mapping the technical structure of a decision analysis
problem to that of Bayesian inference in a purely synthetic "emulating"
statistical model. This provides access to standard posterior analytic,
simulation and optimization methods that yield indirect solutions of the
decision problem. We develop this in time series portfolio analysis using
classes of economically and psychologically relevant multi-step ahead portfolio
utility functions. Studies with multivariate currency, commodity and stock
index time series illustrate the approach and show some of the practical
utility and benefits of the Bayesian emulation methodology.Comment: 24 pages, 7 figures, 2 table
On Solving Robust Log-Optimal Portfolio: A Supporting Hyperplane Approximation Approach
A {log-optimal} portfolio is any portfolio that maximizes the expected
logarithmic growth (ELG) of an investor's wealth. This maximization problem
typically assumes that the information of the true distribution of returns is
known to the trader in advance. However, in practice, the return distributions
are indeed {ambiguous}; i.e., the true distribution is unknown to the trader or
it is partially known at best. To this end, a {distributional robust
log-optimal portfolio problem} formulation arises naturally. While the problem
formulation takes into account the ambiguity on return distributions, the
problem needs not to be tractable in general. To address this, in this paper,
we propose a {supporting hyperplane approximation} approach that allows us to
reformulate a class of distributional robust log-optimal portfolio problems
into a linear program, which can be solved very efficiently. Our framework is
flexible enough to allow {transaction costs}, {leverage and shorting},
{survival trades}, and {diversification considerations}. In addition, given an
acceptable approximation error, an efficient algorithm for rapidly calculating
the optimal number of hyperplanes is provided. Some empirical studies using
historical stock price data are also provided to support our theory.Comment: submitted for possible publicatio
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